Permutation Matrix on Matlab

Question

Zafer Sahin 2021-10-9

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https://ww2.mathworks.cn/matlabcentral/answers/1470496-permutation-matrix-on-matlab

编辑： Zafer Sahin 2022-5-5

Hi I am new on MATLAB. In my project I am using matlab. Some step of works wanted to find permuation matrix. AS you can see from photo given.

So I need to find permutation matrix for A(sc). But I couldn't figure out how to make on MATLAB. I use below codes, it gives irrevalent result. T

A=[-1 -1 1;1 -1 0;-3 0 1;1 0 0]
B = perms(A);

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Answer 1

Walter Roberson 2021-10-9

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The description showed you the way:

ASc = [-1 -1 1;1 -1 0;-3 0 1;1 0 0]
ASc = 4×3
    -1    -1     1
     1    -1     0
    -3     0     1
     1     0     0
[LSc, USc, PSc] = lu(ASc)
LSc = 4×3
    1.0000         0         0
   -0.3333    1.0000         0
    0.3333    1.0000    1.0000
   -0.3333         0    1.0000
USc = 3×3
   -3.0000         0    1.0000
         0   -1.0000    0.3333
         0         0    0.3333
PSc = 4×4
     0     0     1     0
     0     1     0     0
     1     0     0     0
     0     0     0     1

Note: the term "permutation matrix" in this context is not the same as is produced by perms() https://www.mathworks.com/help/matlab/ref/perms.html which "returns a matrix containing all permutations of the elements of vector v in reverse lexicographic order." The concepts do have a relationship, but perms() is not at all what you want for the purpose of building the kind of permutation matrix you need.